As the wiki page states, the period is 133076755768, and it moves by two cells in that time. Spaceships in GoL by definition don’t leave anything behind, they produce the exact same configuration, just shifted across the grid.

Given that it starts as a single line, it is symmetric in the axis implied by that line, and hence can’t possibly move diagonally or orthogonal to the line. Hence it moves in the direction of the line.